Creating channels for network testing using centroids

A network test device may be used by network equipment manufacturers for function, system integration, capacity, and stress testing and emulation of a plurality of mobile devices, across multiple cells, to set up and test network nodes. A network node may be associated with a multi-user multiple-input multiple-output (MU-MIMO) system, which may be a Fourth Generation (4G) system, a Fifth Generation (5G) system, a Sixth Generation (6G) system, and so on. A network test device may deliver voice, data, realistic mobility models, and radio access network and/or physical layer side emulation, thereby providing a comprehensive validation solution. A network test device may ensure that users in a network are obtaining adequate quality of service. A network test device may ensure that the network is satisfying latency and round-trip-time requirements for voice- and time-critical applications.

In some implementations, a method includes generating, using a network test device, a set of candidate points in a spatial frequency domain, wherein a point in the set of candidate points represents a centroid associated with a user equipment (UE); selecting, using the network test device and from the set of candidate points, an initial set of points in the spatial frequency domain that maximizes a minimum distance between pairs of points in the set of candidate points; evaluating, using the network test device, a metric for each point in the initial set of points; adjusting, using the network test device, locations of one or more points in the initial set of points based on metrics associated with the one or more points, to obtain a final set of points in the spatial frequency domain; creating, using the network test device, one or more multiple-input multiple-output (MIMO) channels based on the final set of points; and using, by the network test device, the one or more MIMO channels to test a multiple user MIMO (MU-MIMO) system in a simulation environment.

In some implementations, a network test device includes one or more components configured to: generate a set of candidate points in a spatial frequency domain, wherein a point in the set of candidate points represents a centroid associated with a UE; select, from the set of candidate points, an initial set of points in the spatial frequency domain that maximizes a minimum distance between pairs of points in the set of candidate points; evaluate a metric for each point in the initial set of points; adjust locations of one or more points in the initial set of points based on metrics associated with the one or more points, to obtain a final set of points in the spatial frequency domain; create one or more MIMO channels based on the final set of points; and use the one or more MIMO channels to test a MU-MIMO system in a simulation environment.

In some implementations, a non-transitory computer-readable medium storing a set of instructions includes one or more instructions that, when executed by one or more processors of a network test device, cause the network test device to: generate a set of candidate points in a spatial frequency domain, wherein a point in the set of candidate points represents a centroid associated with a UE; select, from the set of candidate points, an initial set of points in the spatial frequency domain that maximizes a minimum distance between pairs of points in the set of candidate points; evaluate a metric for each point in the initial set of points; adjust locations of one or more points in the initial set of points based on metrics associated with the one or more points, to obtain a final set of points in the spatial frequency domain; create one or more MIMO channels based on the final set of points; and use the one or more MIMO channels to test a MU-MIMO system in a simulation environment.

The following detailed description of example implementations refers to the accompanying drawings. The same reference numbers in different drawings may identify the same or similar elements.

A network test device may be used by network equipment manufacturers for function, system integration, capacity, and stress testing and emulation of a plurality of mobile devices, across multiple cells, to set up and test network nodes. The network test device may deliver voice, data, realistic mobility models, and radio access network and/or physical layer side emulation, thereby providing a comprehensive validation solution.

In a wireless communication system, such as a MU-MIMO system, radio propagation channels may heavily impact system performance metrics, such as signal to interference plus noise ratio (SINR), throughput, and/or block error rate (BLER). By using the network test device, specific channel conditions may be created to evaluate or test the MU-MIMO system. For example, to test whether the MU-MIMO system is able to achieve a maximum throughput, propagation channels may be ensured to allow such data rates. Designing such propagation channels may be a non-trivial, computationally heavy, and/or time consuming task. During the test of the MU-MIMO system, UEs may be placed at optimal angles to create propagation channels which allow for such throughputs. Identifying the optimal angles for the UEs may be a mathematically complex task due to several sources of error and noise, such as calibration error and performance drift due to temperature. An adaptation to system changes by the UEs and/or gNodeBs may add additional complexity when identifying the optimal angles for the UEs. Blindly adjusting UE positions to optimize the throughput may be a tedious and time consuming task. Thus, when testing the MU-MIMO system using existing techniques, an overall system performance of the network test device may be degraded.

In some implementations, in a MU-MIMO system in an open-loop test system, a network test device may use an open-loop centroid based approach for creating MIMO channels with reduced inter-UE interference. The loop centroid based approach may operate independently of information about a gNodeB, such as beam information, or the choice of UE equalizer. Directional channels may be created in the MU-MIMO system in the open-loop test system, which may be useful for a broad set of applications, such as for testing MU-MIMO systems. In a geometry-based model, a channel may be characterized by an antenna array geometry and angles on which UE antennas are placed. Each UE may be modeled by a centroid in a spatial frequency domain. The spatial frequency domain may be used to set directions between each antenna of the UE and a gNodeB. A circular distance between centroids/UEs may be maximized in the spatial frequency domain. Circular and Euclidian distances between angle locations may be maximized in a discrete Fourier transform (DFT) domain. The circular distance (or a different metric to define distance) may be maximized between the centroids. Angles for each UE's antennas may be placed around its centroid. In other words, after the circular distance between different UEs is maximized, the UE's antennas may be placed on directions, such as around the centroid in the spatial frequency domain. A distance to the centroid and a shape of a simplex around the centroid may be optimized so that the UE equalizer is able to effectively correct any distortions. In some implementations, by modeling each UE as the centroid, inter-UE interference may be reduced, thereby improving an overall system performance.

is a diagram of an exampleassociated with a MU-MIMO system in an open-loop test system.

As shown in, in the MU-MIMO system in the open-loop test system, an open-loop algorithm entitymay propose initial UE channels or locations, which may result in a relatively favorable performance. A visualization and processing entitymay visualize or further process such locations and other parameters and reports. The open-loop algorithm entitymay indicate the initial UE channels or locations to a channel command control entity, which may provide the initial UE channels or locations to a MIMO channel emulator and simulator. Performance metrics (e.g., a performance/measurement report) by a gNodeBand UE(s)may be sent to a report collection entity. The report collection entitymay be in connection with other entities in the MU-MIMO system in the open-loop test system, such as the visualization and processing entity.

As indicated above,is provided as an example. Other examples may differ from what is described with regard to.

Regarding an antenna factor and spatial frequency, a downlink scenario may involve K users, where each user has M antennas, and a gNodeB has N antennas. A gNodeB antenna array may be dual polarized and placed on an x-z plane. A transmission on one polarization may be repeated for the other polarization. In each polarization, an array may be a rectangular array with Nantennas with spacing dand Nantennas with don the horizontal and vertical domains. An array response for a received signal y(φ, θ, t)=y(φ, θ, t) a(φ, θ) at position (n, n) in a two-dimensional (2D) array may be represented by:

where n∈ {0, N-1}, n∈ {0, N−1}, t represents a time (t can be dropped for the sake of simplicity of notation), λ is a wavelength, and θ and φ are an elevation angle (angle from a z-axis) and an azimuth angle (angle from an x-axis in the yz-plane), respectively. A relationship between phase values on a phase shifter matrix and UE locations may also be in accordance with the array response.

Signals can be represented by an array response matrix A(φ, θ) where it's elements is generated using a(φ, θ). Instead of using the elevation and azimuth angles, UE locations may be represented using spatial frequency and in a DFT domain. However, other transforms that capture a linear progressive phase effect over the array may be used. Using spatial frequency in antenna array processing may introduce linearity in the manner in which the array's response to signals from different directions is represented and analyzed. Such linearity may arise from a relationship between an array geometry, signal arrival angles, and Fourier transform properties.

Spatial frequencies may be defined as ω=2 πf/Nand ω=2 πf/N, where normalized spatial frequencies fand fare continuous and periodic with periodicities Nand N, respectively. For the x-axis,

may be assumed, and the notation for the y-axis may be similar. A spatial frequency response of the array is defined by:

which may be used for any array excitation and beam parameters a.

Regarding Euclidean distances versus circular distances, in a two-dimensional space, two points a=(x, y) and b=(x, y) on a grid may be considered with boundaries [−N, N] for an x-axis and [−M, M] for a y-axis. Due to a periodic behavior of a spatial frequency, a circular distance may be used instead of a Euclidean distance. The Euclidean distance may be a direct distance between two points in a straight line. The Euclidean distance may always be a shortest distance between the two points when there are no grid boundaries to consider. The Euclidean distance may be defined as:

On the other hand, the circular distance may consider a possibility of wrapping around the boundaries of the grid. In effect, the circular distance may sometimes provide a shorter path by wrapping around the edges. The circular distance may be either equal to or shorter than the Euclidean distance, depending on positions of points and dimensions of a grid. The circular distance may be defined as:

is a diagram of an exampleassociated with creating channels for network testing using centroids. The exampleincludes a network test device.

As shown by reference number, the network test devicemay generate a set of candidate points in a spatial frequency domain. A point in the set of candidate points may represent a centroid associated with a UE. The centroid may be a center point associated with the UE, where the centroid may be represented in the spatial frequency domain. The network test devicemay generate the set of candidate points in a first step of a two-step algorithm.

As shown by reference number, the network test devicemay select, from the set of candidate points, an initial set of points in the spatial frequency domain that maximizes a minimum distance between pairs of points in the set of candidate points. The network test devicemay select the initial set of points in the first step of the two-step algorithm. The network test devicemay compute distances between the pairs of points in the set of candidate points. The initial set of points may be based on the distances between the pairs of points. The minimum distance may be a circular distance. The network test devicemay maximize the minimum distance between the pairs of points in the set of candidate points to reduce inter-UE interference.

As shown by reference number, the network test devicemay evaluate a metric for each point in the initial set of points. The metric may be an average SINR. Alternatively, the network test devicemay evaluate another type of metric, such as a minimum SINR or a channel condition number. The network test devicemay evaluate the metric in a second step of the two-step algorithm.

As shown by reference number, the network test devicemay adjust locations of one or more points in the initial set of points based on metrics associated with the one or more points, to obtain a final set of points in the spatial frequency domain. The network test devicemay adjust the locations, to obtain the final set of points, in the second step of the two-step algorithm.

In some implementations, the network test devicemay use an open-loop centroid based approach for creating MIMO channels, which may not exploit gNodeB beam information. The open-loop centroid based approach may be based at least in part on the two-step algorithm. The network test devicemay use the two-step algorithm to find an optimal initial set of coordinates for points within a defined 2D region, such that a minimum distance between any two points is maximized, where such an optimization may help ensure that points are relatively well spaced. The points may be associated with UE locations. The first step of the two-step algorithm may involve an initial placement. As part of the initial placement, the network test devicemay generate candidate locations. The network test devicemay generate a set of potential initial coordinates within the defined 2D region. Potential initial coordinates may correspond to initial UE locations. The network test devicemay calculate distances. The network test devicemay compute the distance between each pair of candidate points. The network test devicemay select an initial set. The network test devicemay select an initial set of points that maximizes a minimum distance between any two points. The second step of the two-step algorithm may involve an iterative optimization. As part of the iterative optimization, the network test devicemay evaluate a performance. For each selected point, the network test devicemay evaluate performance criteria (e.g., average SINR). The network test devicemay adjust locations. The network test devicemay iteratively adjust the points' positions to further improve spacing and performance, which may ensure that the points remain within the defined 2D region. The network test devicemay finalize coordinates. The network test devicemay finalize the coordinates when no further improvement in spacing or performance can be achieved. The network test devicemay utilize the two-step algorithm to ensure that the points are optimally spaced within the defined 2D region, providing a good initial setup for further optimizations.

In some implementations, during the first step of the two-step algorithm, the network test devicemay maximize the minimum distance between the centroid of the UE in a DFT domain to minimize inter-UE interference. The network test devicemay model each multiantenna UE k by its centroid spatial frequency, which may be defined by F=(F, F), where

and fand fare the horizontal and vertical spatial frequencies corresponding to an l-th layer of user k, respectively. Further,

A design criteria may be to maximize Δ(F), where:

In some implementations, to solve this optimization problem, the network test devicemay utilize an algorithm for maximizing a minimum distance. An input to the algorithm may be N, N, K, numIter, tolerance, and an output of the algorithm may be F, δ. The network test device, when running the algorithm, may initialize δ=−1, t=∞. For i=1:numIter, the network test devicemay generate F such that

When

While

where Ψ{Δ} may represent applying an optimization method, such as a Nelder Mead or Hooke-Jeeves pattern search, to find the local or global optima of Δ. The network test devicemay update Fby considering a circular wrap around effect when any elements of Fare outside grid boundaries. Further, t=|δ−δ| and

U(0,1) may represent a uniform random variable between 0 and 1.

In some implementations, during the second step of the two-step algorithm, after centroids are calculated, the network test devicemay place each UE's angles (or antennas) around its centroid. A shape and distance of these angles may depend on a performance of gNodeB beams, an array structure, a UE equalizer, and/or an intra-UE interference among its layers. The network test devicemay separate UE angles in a vertical domain, which may be due to the gNodeB offering more directional beams in the vertical domain due to its larger antenna spacing as compared to a horizontal domain. L and r may denote a number of layers per polarization for a given UE, and a distance of an lth layer to a centroid F, respectively. The network test devicemay place the UE angles around its centroid according to:

where pis defined by:

In some implementations, in the two-step algorithm, a number transmit layers (or transmission layers) may be assumed to be an even number, but a generalization to odd numbers may be straightforward.

As shown by reference number, the network test devicemay create one or more MIMO channels based on the final set of points. The network test devicemay create the one or more MIMO channels without using network node information (e.g., base station information) that includes beam information. The network test devicemay create the one or more MIMO channels without using UE equalizer information. The network test devicemay create the one or more MIMO channels based on a number of UEs, a polarization, and a number of layers per polarization for a given UE. The network test devicemay create multiple MIMO channels for multiple UEs, where each UE of the multiple UEs may be associated with a certain number of layers per polarization.

As shown by reference number, the network test devicemay use the one or more MIMO channels to test a MU-MIMO system in a simulation environment. The network test device, using the one or more MIMO channels, may evaluate whether the MU-MIMO system is able to achieve a maximum throughput. The network test devicemay create such directional channels within the simulation environment, where the directional channels may be evaluated in terms of system performance metrics, such as SINR, throughput, and/or BLER. In some implementations, the network test devicemay place, within the simulation environment, one or more antennas associated with the UE in directions surrounding the centroid in the spatial frequency domain. The one or more antennas may be placed in accordance with an array structure associated with the one or more antennas.

As indicated above,is provided as an example. Other examples may differ from what is described with regard to.

is a diagram of an exampleassociated with algorithm outputs.

In some implementations, an algorithm output may consider different combinations of a number of UEs (K), transit layers, and polarization. As shown by reference number, K=2, polarization=1, and layers per polarization=4. As shown, each of the two centroids (2 UEs) may be associated with four layers per polarization (UE per layer location). As shown by reference number, K=2, polarization=2, and layers per polarization=2. As shown, each of the two centroids (2 UEs) may be associated with two layers per polarization (UE per layer location).

As indicated above,is provided as an example. Other examples may differ from what is described with regard to.

is a diagram of an exampleassociated with algorithm outputs.

In some implementations, an algorithm output may consider different combinations of a number of UEs (K), transit layers, and polarization. As shown by reference number, K=2, polarization=1, and layers per polarization=4. As shown, each of the four centroids (4 UEs) may be associated with four layers per polarization (UE per layer location). As shown by reference number, K=3, polarization=2, and layers per polarization=2. As shown, each of the three centroids (3 UEs) may be associated with two layers per polarization (UE per layer location).

As indicated above,is provided as an example. Other examples may differ from what is described with regard to.

is a diagram of an exampleassociated with algorithm outputs.

In some implementations, an algorithm output may consider different combinations of a number of UEs (K), transit layers, and polarization. As shown by reference number, K=4, polarization=1, and layers per polarization=8. As shown, each of the four centroids (4 UEs) may be associated with eight layers per polarization (UE per layer location). As shown by reference number, K=4, polarization=2, and layers per polarization=2. As shown, each of the four centroids (4 UEs) may be associated with two layers per polarization (UE per layer location).